Extremely stubborn broody - what next?

[RoyalChick]

I have a very stubborn broody. She has spent most of the summer being broody. I have a dog crate set up as a broody jail and most of the summer it has taken 3-4 spells of 3-4 days each for her to break. Then she is normal for a week. Starts to lay and immediately goes broody again.
It is definitely Fall here - night time temperatures are dropping into the mid 50s and her jail is in the entryway between the coop and the secure run - so she is definitely getting a cool breeze all around her.
It is as if she knows this is her last chance of the season and is digging in. I cannot break her this time. I tend to let her out on a trial every 3-4 days but she goes straight back to the nest - I think we are at 12 days in jail now.
Is there anything else I can do?
A related question is how many days in a row would you keep her in jail? I have felt that it is better she get out now and then to dust bathe. I carry her a long way from the coop and if I am lucky she stops for a bath and maybe a snack before going to the nest.
All suggestions welcome, but for various reasons having her hatch or raise day-olds is not practical for me right now.
@aart - I think my broody jail is based on your design - have you ever had this issue?

Pictures of my set up below - the cage is actually suspended from the ceiling in chains.

 

[aart]

@aart - I think my broody jail is based on your design - have you ever had this issue?

Yep, I have one that takes 3-4 days to break, then quickly goes broody again. I think she went broody 4 or 5 times this summer.
She also can't have the floor roost as she hunkers down and tries to 'hatch' it.

 

[RoyalChick]

Yep, I have one that takes 3-4 days to break, then quickly goes broody again. I think she went broody 4 or 5 times this summer.
She also can't have the floor roost as she hunkers down and tries to 'hatch' it.

Thanks for responding.
Yes, she is definitely trying to hatch the 2x4 - but I worry about the wire on her feet. I thought in your set-up you gave them a small piece of wood to stand on.
Do yours really stand directly on the dog crate wire?
Also, how long do you think it is OK to keep her in there without releasing her at all? So far, I haven’t gone past 4 days before giving her a run outside. Do you do more than that?
Tassels has been caged for 2x 4 days this time and she is still as broody as they come.